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Simplifying Algebraic Expressions: A Step-by-Step Guide
In mathematics, simplifying algebraic expressions is a fundamental skill. This involves combining like terms and reducing the expression to its simplest form. Let's explore how to simplify the expression: (2ab² + 2a³b - 4ab) + (4a²b - 3ab - 2a²b)
Understanding Like Terms
Before we begin, it's crucial to understand what constitutes like terms. Like terms have the same variables raised to the same powers. For example:
- 2ab² and -4ab are not like terms because the 'b' term has different exponents.
- 2a³b and 4a²b are not like terms because the 'a' term has different exponents.
- 4a²b and -2a²b are like terms because they have the same variables raised to the same powers.
Simplifying the Expression
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Remove the Parentheses: Since we are adding the two expressions, the parentheses do not change the order of operations. Therefore, we can simply remove them:
2ab² + 2a³b - 4ab + 4a²b - 3ab - 2a²b
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Identify Like Terms: Now, we group the like terms together:
(2ab² ) + (2a³b) + (-4ab - 3ab) + (4a²b - 2a²b)
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Combine Like Terms: Add or subtract the coefficients of the like terms:
2ab² + 2a³b - 7ab + 2a²b
Final Simplified Expression
The simplified form of the expression (2ab² + 2a³b - 4ab) + (4a²b - 3ab - 2a²b) is 2ab² + 2a³b - 7ab + 2a²b.
Key Takeaways
- Identify like terms: This is the first step in simplifying any algebraic expression.
- Combine like terms: Add or subtract the coefficients of the like terms, keeping the variables and exponents the same.
- Order doesn't matter: You can rearrange the terms in any order as long as the signs remain the same.
By following these steps, you can confidently simplify algebraic expressions and reach the correct solution.